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Model-based clustering via new parsimonious mixtures of heavy-tailed distributions

Author

Listed:
  • Salvatore D. Tomarchio

    (Università degli Studi di Catania)

  • Luca Bagnato

    (Università Cattolica del Sacro Cuore)

  • Antonio Punzo

    (Università degli Studi di Catania)

Abstract

Two families of parsimonious mixture models are introduced for model-based clustering. They are based on two multivariate distributions-the shifted exponential normal and the tail-inflated normal-recently introduced in the literature as heavy-tailed generalizations of the multivariate normal. Parsimony is attained by the eigen-decomposition of the component scale matrices, as well as by the imposition of a constraint on the tailedness parameters. Identifiability conditions are also provided. Two variants of the expectation-maximization algorithm are presented for maximum likelihood parameter estimation. Parameter recovery and clustering performance are investigated via a simulation study. Comparisons with the unconstrained mixture models are obtained as by-product. A further simulated analysis is conducted to assess how sensitive our and some well-established parsimonious competitors are to their own generative scheme. Lastly, our and the competing models are evaluated in terms of fitting and clustering on three real datasets.

Suggested Citation

  • Salvatore D. Tomarchio & Luca Bagnato & Antonio Punzo, 2022. "Model-based clustering via new parsimonious mixtures of heavy-tailed distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 315-347, June.
    • Handle: RePEc:spr:alstar:v:106:y:2022:i:2:d:10.1007_s10182-021-00430-8
    DOI: 10.1007/s10182-021-00430-8
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    12. Francesca Greselin & Salvatore Ingrassia & Antonio Punzo, 2011. "Assessing the pattern of covariance matrices via an augmentation multiple testing procedure," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(2), pages 141-170, June.
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    Cited by:

    1. Katharine M. Clark & Paul D. McNicholas, 2024. "Finding Outliers in Gaussian Model-based Clustering," Journal of Classification, Springer;The Classification Society, vol. 41(2), pages 313-337, July.

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